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Results tagged with enriched-category-theory
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user 4262
0
votes
Is there a sensible way to enrich over SymMonCat such that id_X is not the monoidal unit?
A monoidal functor preserves the unit and tensor only 'laxly', so that $1_X$ is not the local unit but comes with a 2-cell $I \Rightarrow 1_X$.
If you're talking about strong monoidal functors then e …
- 3,622
3
votes
When does the 2-category V-Cat have pseudo-pullbacks?
I'm presuming that you want to treat V-Cat as a 2-category rather than as a V-category. There might be a slick change-of-base argument that applies here, but I can't think of one. I think the answer …
- 3,622
8
votes
2
answers
469
views
Reference request: (co)limits in Eilenberg--Moore (V-)categories
The following result seems to be well known:
If T is a (V-)monad on a (V-)category C, then the forgetful functor $U^T \colon C^T \to C$ creates
any limits that exist in C, and
any colimits that exis …
- 3,622
12
votes
Accepted
Definition of enriched caterories or internal homs without using monoidal categories.
This is exactly the notion of a closed category. See Eilenberg and Kelly's article in the 1965 La Jolla proceedings (Springer 1966). I think they also describe categories enriched in a closed catego …
- 3,622
3
votes
Accepted
Reference Request(Enriched Categories): Metric on Lipschitz Continuous Functions
It is the usual sup metric. See section 2 of Lawvere's original article.
- 3,622